Let n be a positive integer. Consider a figure of a equilateral triangle of side n and splitted in n2 small equilateral triangles of side 1. One will mark some of the 1+2+⋯+(n+1) vertices of the small triangles, such that for every integer k≥1, there is not any trapezoid(trapezium), whose the sides are (1,k,1,k+1), with all the vertices marked. Furthermore, there are no small triangle(side 1) have your three vertices marked. Determine the greatest quantity of marked vertices.